Question

If each element of a $3\times 3$ matrix is multiplied by $3$, then the determinant of the newly formed matrix is

• A. $3\left|A\right|$
• B. $9\left|A\right|$
• C. $27\left|A\right|$
• D. ${\left|A\right|}^3$

Answer 1

Answer: (C)

$27\left|A\right|$

Let the $3\times 3$ matrix be $A$.
Since, each element of matrix $A$ is multiplied by $3$, therefore we can have matrix as,
$3\times 3\times 3|A|$ $=27|A|$